Abstract
In the 1980s, Zagier and Jacquet and Zagier tried to derive the Selberg trace formula by applying the RankinâSelberg method to the automorphic kernel function. Their derivation was incomplete due to a puzzle of the computation of a residue. We solve this puzzle and complete the derivation. The main input is an extension of the theory of regularized integrals invented by Zagier, which is of independent interest.
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